Points of integral canonical models of Shimura varieties of preabelian type, pdivisible groups, and applications. First Part
Abstract
This work is the first part in a series of three dedicated to the foundations of integral aspects of Shimura varieties and of Fontaine's categories. It deals mostly with the unramified context of (arbitrary) mixed characteristic (0,p). Among the topics covered we mention: the generalization of the classical SerreTate theory of ordinary pdivisible groups and of their canonical lifts, the generalization of the classical SerreTateDworkKatz theory of (crystalline) coordinates for ordinary abelian varieties, the strong form of the generalized Manin problem, global deformations in the generalized Shimura context, Dieudonné's theories (reobtained, simplified and extended), the main list of stratifications of special fibres of integral canonical models of Shimura varieties of preabelian type, the uniqueness of such models in mixed characteristic (0,2), the existence (in many situations) of such models in mixed characteristic (0,2), steps towards the classification of Shimura pdivisible groups over algebraically closed field of characteristic p (like the boundedness principle, the purity principle, Bruhat decompositions in the Fcontext, etc.), generalized Serre lemma, connections in Fontaine's categories, etc.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2001
 arXiv:
 arXiv:math/0104152
 Bibcode:
 2001math......4152V
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G10;
 11G18;
 11G25;
 11G35;
 14F30;
 14G35;
 14K10
 EPrint:
 595 pages